Soundproofing relies mainly on density and completeness. On the matter of completeness if there is a c.10% gap about c.80-90% of the soundproofing benefit may be lost. For this reason many DIY attempts fail.
Sound can tansmit in various ways and any soundproof room must eliminate all forms of sound transference.
Pete's idea is good in principle, but not necessarily practical.
The soundproof 'booth' must be of sufficient density to keep sound in, must be isolated from surrounding material to stop transference through material, and must be complete with no gaps so that there is no direct or flanking sound. You could install a free-standing booth in a room or you could create a soundproof room.
For dividing floors/ceilings there are a number of products on the market some of which can be retro-fitted and some involve more or less reconstruction. Generally however you create a sandwich of a dense board with isolating mounts and then an accoustic insulant in all voids above with the floor above on an isolating layer (see attached sketch - simplified) to give you the idea.
The same principle applies to the floor and walls. Use dense materials but isolate them - rubber based materials can be good, but proprietary 'resilient bars' are now usually used together with accoustic mats. Use accoustic insulation to stuff ALL gaps to stop flanking sound. Don't forget to check floor voids to see if there are gaps in walls in hidden areas, gaps around pipes or cables, etc, etc.
If using concrete make sure the surface finish is sound absorbent otherwise it could become an echo chamber! In fact all surfaces in a soundproof area should be absorbent (e.g. put thick carpet on the floor and walls and ceiling if you cannot afford proprietary accoustic mats).
The above are just a few simple 'guides' but you could look at websites such as :
http://www.rockwool.co.uk/acoustic/introduction
where there is quite a bit of information.
The following sites may also help:
JCW Acoustic Supplies - Home
CMS Danskin Acoustics Refurbishment Division - CMS Danskin Acoustics
Soundproofing Solutions| Domestic Soundproofing | SRS
I hope the above gives some indication of what is involved to create a soundproof room.
Cellars can be a problem in that they are often damp (not in Germany however, or in other countries where cellars have to be habitable rooms). The damp can ruin some of the boards, etc used for sound proofing and over time the benefit will rot away! Other materials (some barriers, etc) are themselves damp proof and could create problems by diverting moisture and this can create problems eslewhere. Damp proofing cellars is a whole different subject. I have written articles and given lectures on it - so doubt you want boring on the subject now!
Generally it can be a lot of hassle and cost. Far better (and cheaper) to play when neighbours are out.
SLoB